Problem: Ashley is 3 times as old as Vanessa. Sixteen years ago, Ashley was 7 times as old as Vanessa. How old is Ashley now?
Answer: We can use the given information to write down two equations that describe the ages of Ashley and Vanessa. Let Ashley's current age be $a$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $a = 3v$ Sixteen years ago, Ashley was $a - 16$ years old, and Vanessa was $v - 16$ years old. The information in the second sentence can be expressed in the following equation: $a - 16 = 7(v - 16)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $a$ , it might be easiest to solve our first equation for $v$ and substitute it into our second equation. Solving our first equation for $v$ , we get: $v = a / 3$ . Substituting this into our second equation, we get: $a - 16 = 7($ $(a / 3)$ $- 16)$ which combines the information about $a$ from both of our original equations. Simplifying the right side of this equation, we get: $a - 16 = \dfrac{7}{3} a - 112$ Solving for $a$ , we get: $\dfrac{4}{3} a = 96$ $a = \dfrac{3}{4} \cdot 96 = 72$.